Model independent reconstruction of impact parameter distributions for intermediate energy heavy ion collisions

We present a model-independent method to reconstruct the impact parameter distributions of experimental data for intermediate energy heavy ion collisions, adapted from a recently proposed approach for ultra-relativistic heavy ion collisions. The method takes into account the fluctuations which are inherent to the relationship between any experimental observable and the impact parameter in this energy range. We apply the method to the very large dataset on heavy ion collisions in the energy range 20-100 MeV/nucleon obtained with the INDRA multidetector since 1993, for two observables which are the most commonly used for the estimation of impact parameters in this energy range. The mean impact parameters deduced with this new method for "central" collisions selected using typical observable cuts are shown to be significantly larger than those found when fluctuations are neglected, and as expected the difference increases as bombarding energy decreases. In addition, we will show that this new approach may provide previously inaccessible experimental constraints for transport models, such as an estimation of the extrapolated mean value of experimental observables for b = 0 collisions. The ability to give more realistic, model-independent, estimations of the impact parameters associated to different experimental datasets should improve the pertinence of comparisons with transport model calculations which are essential to better constrain the equation of state of nuclear matter.